##############ECHO OF PROBLEM################# ##############temp/lin_arccospostode.ode################# diff ( y , x , 1 ) = arccos ( 0.1 * x + 0.2 ) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-0.8); x_end=c(0.8); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=0; array_given_rad_poles[1][1]=c(0.0); array_given_rad_poles[1][2]=c(1.0); array_given_ord_poles[1][1]=c(1.0); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arccos(c(0.1) * c(x) + c(0.2) )-c(10.0) * sqrt(c(1.0) - expt((c(0.1) * c(x) + c(0.2)) , c(2) ))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (closed_form) = -8.187131183512555 y[1] (numeric) = -8.187131183512555 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (closed_form) = -8.172631155666924 y[1] (numeric) = -8.17263115566487 absolute error = 2.05346850634669e-12 relative error = 2.512616154129027e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (closed_form) = -8.158141201840962 y[1] (numeric) = -8.158141201836838 absolute error = 4.124700581087382e-12 relative error = 5.055931834272007e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (closed_form) = -8.143661323277081 y[1] (numeric) = -8.143661323270871 absolute error = 6.210143510543276e-12 relative error = 7.625738920149811e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.76 y[1] (closed_form) = -8.129191521228385 y[1] (numeric) = -8.129191521220068 absolute error = 8.316902722071973e-12 relative error = 1.02309100485004e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.75 y[1] (closed_form) = -8.114731796958676 y[1] (numeric) = -8.114731796948233 absolute error = 1.044320185883407e-11 relative error = 1.286943563895493e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.74 y[1] (closed_form) = -8.100282151742475 y[1] (numeric) = -8.100282151729891 absolute error = 1.258371185031137e-11 relative error = 1.553490559289278e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.73 y[1] (closed_form) = -8.085842586865027 y[1] (numeric) = -8.085842586850287 absolute error = 1.474020905334328e-11 relative error = 1.822965126391142e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (closed_form) = -8.071413103622319 y[1] (numeric) = -8.071413103605398 absolute error = 1.692157525212679e-11 relative error = 2.096482367447239e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.71 y[1] (closed_form) = -8.05699370332108 y[1] (numeric) = -8.056993703301968 absolute error = 1.911182323510729e-11 relative error = 2.37207871060262e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (closed_form) = -8.042584387278817 y[1] (numeric) = -8.042584387257492 absolute error = 2.132516385700001e-11 relative error = 2.651531252905549e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6899999999999999 y[1] (closed_form) = -8.028185156823803 y[1] (numeric) = -8.028185156800241 absolute error = 2.356159711780492e-11 relative error = 2.934859704596875e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6799999999999999 y[1] (closed_form) = -8.013796013295094 y[1] (numeric) = -8.013796013269287 absolute error = 2.580691216280684e-11 relative error = 3.220310589387665e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6699999999999999 y[1] (closed_form) = -7.999416958042559 y[1] (numeric) = -7.999416958014485 absolute error = 2.807443166830126e-11 relative error = 3.509559736109944e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6599999999999999 y[1] (closed_form) = -7.985047992426874 y[1] (numeric) = -7.985047992396512 absolute error = 3.036149109902908e-11 relative error = 3.802292876363965e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6499999999999999 y[1] (closed_form) = -7.970689117819537 y[1] (numeric) = -7.970689117786875 absolute error = 3.266276138447211e-11 relative error = 4.097859156424775e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6399999999999999 y[1] (closed_form) = -7.956340335602894 y[1] (numeric) = -7.956340335567911 absolute error = 3.498268341672883e-11 relative error = 4.396830947538648e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6299999999999999 y[1] (closed_form) = -7.942001647170137 y[1] (numeric) = -7.942001647132815 absolute error = 3.732214537421896e-11 relative error = 4.699337400353907e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6199999999999999 y[1] (closed_form) = -7.927673053925329 y[1] (numeric) = -7.927673053885647 absolute error = 3.96820354353622e-11 relative error = 5.005508572999732e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6099999999999999 y[1] (closed_form) = -7.913354557283403 y[1] (numeric) = -7.913354557241345 absolute error = 4.205880088647973e-11 relative error = 5.314914248062987e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5999999999999999 y[1] (closed_form) = -7.899046158670194 y[1] (numeric) = -7.89904615862574 absolute error = 4.445332990599127e-11 relative error = 5.627683268719497e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5899999999999999 y[1] (closed_form) = -7.884747859522434 y[1] (numeric) = -7.884747859475569 absolute error = 4.686473431547711e-11 relative error = 5.94372009738757e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5799999999999998 y[1] (closed_form) = -7.87045966128778 y[1] (numeric) = -7.870459661238485 absolute error = 4.929567865019635e-11 relative error = 6.263379875087308e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5699999999999998 y[1] (closed_form) = -7.856181565424819 y[1] (numeric) = -7.856181565373075 absolute error = 5.17443865533096e-11 relative error = 6.586455025560696e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5599999999999998 y[1] (closed_form) = -7.841913573403087 y[1] (numeric) = -7.841913573348876 absolute error = 5.421085802481684e-11 relative error = 6.91296295443504e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5499999999999998 y[1] (closed_form) = -7.827655686703078 y[1] (numeric) = -7.827655686646382 absolute error = 5.669686942155749e-11 relative error = 7.243148100889141e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5399999999999998 y[1] (closed_form) = -7.813407906816265 y[1] (numeric) = -7.813407906757064 absolute error = 5.920064438669215e-11 relative error = 7.576801965637384e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5299999999999998 y[1] (closed_form) = -7.799170235245104 y[1] (numeric) = -7.799170235183381 absolute error = 6.17221829202208e-11 relative error = 7.91394226033086e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5199999999999998 y[1] (closed_form) = -7.78494267350306 y[1] (numeric) = -7.784942673438798 absolute error = 6.426237320056316e-11 relative error = 8.254700888073007e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5099999999999998 y[1] (closed_form) = -7.770725223114614 y[1] (numeric) = -7.770725223047792 absolute error = 6.682121522771922e-11 relative error = 8.599096391795508e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4999999999999998 y[1] (closed_form) = -7.756517885615279 y[1] (numeric) = -7.75651788554588 absolute error = 6.939870900168899e-11 relative error = 8.947147421704681e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4899999999999998 y[1] (closed_form) = -7.742320662551613 y[1] (numeric) = -7.74232066247962 absolute error = 7.199307816563305e-11 relative error = 9.298643301336283e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4799999999999998 y[1] (closed_form) = -7.728133555481238 y[1] (numeric) = -7.728133555406633 absolute error = 7.460521089797112e-11 relative error = 9.653716562009568e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4699999999999998 y[1] (closed_form) = -7.713956565972856 y[1] (numeric) = -7.713956565895617 absolute error = 7.723865991238199e-11 relative error = 1.001284609937921e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4599999999999997 y[1] (closed_form) = -7.699789695606253 y[1] (numeric) = -7.699789695526364 absolute error = 7.988987249518686e-11 relative error = 1.037559149709953e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4499999999999997 y[1] (closed_form) = -7.68563294597233 y[1] (numeric) = -7.685632945889769 absolute error = 8.256062500322514e-11 relative error = 1.074220244234942e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4399999999999997 y[1] (closed_form) = -7.6714863186731 y[1] (numeric) = -7.671486318587853 absolute error = 8.524736472281802e-11 relative error = 1.111223577565642e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4299999999999997 y[1] (closed_form) = -7.657349815321725 y[1] (numeric) = -7.65734981523377 absolute error = 8.7954532546064e-11 relative error = 1.148628894687222e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4199999999999997 y[1] (closed_form) = -7.643223437542514 y[1] (numeric) = -7.643223437451832 absolute error = 9.068212847296309e-11 relative error = 1.186438277174318e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4099999999999997 y[1] (closed_form) = -7.629107186970943 y[1] (numeric) = -7.629107186877517 absolute error = 9.342571161141677e-11 relative error = 1.224595608919613e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3999999999999997 y[1] (closed_form) = -7.615001065253674 y[1] (numeric) = -7.615001065157487 absolute error = 9.618705831826446e-11 relative error = 1.263125999511075e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3899999999999997 y[1] (closed_form) = -7.600905074048573 y[1] (numeric) = -7.600905073949604 absolute error = 9.896883312876525e-11 relative error = 1.302066427150499e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3799999999999997 y[1] (closed_form) = -7.586819215024715 y[1] (numeric) = -7.586819214922945 absolute error = 1.017701478644994e-10 relative error = 1.341407314187174e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3699999999999997 y[1] (closed_form) = -7.572743489862411 y[1] (numeric) = -7.572743489757824 absolute error = 1.045874498117882e-10 relative error = 1.381103822568385e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3599999999999997 y[1] (closed_form) = -7.558677900253223 y[1] (numeric) = -7.558677900145797 absolute error = 1.074251798627301e-10 relative error = 1.421216531255172e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3499999999999996 y[1] (closed_form) = -7.544622447899971 y[1] (numeric) = -7.544622447789689 absolute error = 1.102815616604857e-10 relative error = 1.461724061370127e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3399999999999996 y[1] (closed_form) = -7.530577134516765 y[1] (numeric) = -7.530577134403607 absolute error = 1.131574833834748e-10 relative error = 1.502640254022656e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3299999999999996 y[1] (closed_form) = -7.516541961829004 y[1] (numeric) = -7.516541961712953 absolute error = 1.160511686748578e-10 relative error = 1.543943601515117e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3199999999999996 y[1] (closed_form) = -7.50251693157341 y[1] (numeric) = -7.502516931454446 absolute error = 1.189643938914742e-10 relative error = 1.585659785595782e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3099999999999996 y[1] (closed_form) = -7.488502045498028 y[1] (numeric) = -7.488502045376132 absolute error = 1.218962708549043e-10 relative error = 1.627779095395807e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2999999999999996 y[1] (closed_form) = -7.474497305362258 y[1] (numeric) = -7.474497305237411 absolute error = 1.248467995651481e-10 relative error = 1.670303626647669e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2899999999999996 y[1] (closed_form) = -7.460502712936863 y[1] (numeric) = -7.460502712809046 absolute error = 1.278168682006253e-10 relative error = 1.713247392551508e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2799999999999996 y[1] (closed_form) = -7.446518270003987 y[1] (numeric) = -7.446518269873183 absolute error = 1.308047004044965e-10 relative error = 1.75658872592045e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2699999999999996 y[1] (closed_form) = -7.432543978357177 y[1] (numeric) = -7.432543978223366 absolute error = 1.338111843551815e-10 relative error = 1.800341642711112e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2599999999999996 y[1] (closed_form) = -7.418579839801397 y[1] (numeric) = -7.418579839664558 absolute error = 1.368389845879392e-10 relative error = 1.844544205803176e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2499999999999996 y[1] (closed_form) = -7.404625856153042 y[1] (numeric) = -7.404625856013158 absolute error = 1.398836602106712e-10 relative error = 1.889138802258749e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2399999999999995 y[1] (closed_form) = -7.390682029239967 y[1] (numeric) = -7.390682029097017 absolute error = 1.429496521154761e-10 relative error = 1.934187556032315e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2299999999999995 y[1] (closed_form) = -7.376748360901489 y[1] (numeric) = -7.376748360755458 absolute error = 1.460307430534158e-10 relative error = 1.979608574252217e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2199999999999995 y[1] (closed_form) = -7.362824852988426 y[1] (numeric) = -7.362824852839291 absolute error = 1.491358148086874e-10 relative error = 2.025524411981036e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2099999999999995 y[1] (closed_form) = -7.348911507363089 y[1] (numeric) = -7.34891150721083 absolute error = 1.522586501323531e-10 relative error = 2.071853089805214e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1999999999999995 y[1] (closed_form) = -7.33500832589932 y[1] (numeric) = -7.335008325743921 absolute error = 1.553992490244127e-10 relative error = 2.118596763901556e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1899999999999995 y[1] (closed_form) = -7.32111531048251 y[1] (numeric) = -7.321115310323946 absolute error = 1.585638287338043e-10 relative error = 2.165842525479275e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1799999999999995 y[1] (closed_form) = -7.307232463009601 y[1] (numeric) = -7.307232462847858 absolute error = 1.617435074763307e-10 relative error = 2.213471492731381e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1699999999999995 y[1] (closed_form) = -7.293359785389122 y[1] (numeric) = -7.29335978522418 absolute error = 1.649427261440906e-10 relative error = 2.261546543672812e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1599999999999995 y[1] (closed_form) = -7.279497279541203 y[1] (numeric) = -7.279497279373042 absolute error = 1.681605965586641e-10 relative error = 2.310057825439047e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1499999999999995 y[1] (closed_form) = -7.265644947397586 y[1] (numeric) = -7.265644947226188 absolute error = 1.713980068984711e-10 relative error = 2.359019854938859e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1399999999999995 y[1] (closed_form) = -7.251802790901658 y[1] (numeric) = -7.251802790727002 absolute error = 1.746567335203508e-10 relative error = 2.408459503883375e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1299999999999994 y[1] (closed_form) = -7.237970812008458 y[1] (numeric) = -7.237970811830523 absolute error = 1.77935000067464e-10 relative error = 2.45835476114733e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1199999999999994 y[1] (closed_form) = -7.224149012684695 y[1] (numeric) = -7.224149012503465 absolute error = 1.812301420045515e-10 relative error = 2.508671148481768e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1099999999999994 y[1] (closed_form) = -7.210337394908786 y[1] (numeric) = -7.210337394724237 absolute error = 1.845483765805511e-10 relative error = 2.55949710079948e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.09999999999999942 y[1] (closed_form) = -7.19653596067085 y[1] (numeric) = -7.196535960482968 absolute error = 1.878825983681054e-10 relative error = 2.610736601538377e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.08999999999999941 y[1] (closed_form) = -7.182744711972754 y[1] (numeric) = -7.182744711781514 absolute error = 1.912399127945719e-10 relative error = 2.662490739449481e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.0799999999999994 y[1] (closed_form) = -7.168963650828103 y[1] (numeric) = -7.168963650633491 absolute error = 1.946123262541732e-10 relative error = 2.714650760318657e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.0699999999999994 y[1] (closed_form) = -7.155192779262291 y[1] (numeric) = -7.155192779064284 absolute error = 1.980069441742671e-10 relative error = 2.767318090270684e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.05999999999999939 y[1] (closed_form) = -7.141432099312498 y[1] (numeric) = -7.141432099111074 absolute error = 2.014237665548535e-10 relative error = 2.820495437802237e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.04999999999999938 y[1] (closed_form) = -7.12768161302772 y[1] (numeric) = -7.127681612822863 absolute error = 2.048574643254142e-10 relative error = 2.874110762060178e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.03999999999999937 y[1] (closed_form) = -7.113941322468791 y[1] (numeric) = -7.11394132226048 absolute error = 2.083107020212083e-10 relative error = 2.928203826524071e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.02999999999999936 y[1] (closed_form) = -7.100211229708398 y[1] (numeric) = -7.100211229496614 absolute error = 2.117843678206555e-10 relative error = 2.9827896800382e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.01999999999999935 y[1] (closed_form) = -7.086491336831104 y[1] (numeric) = -7.086491336615826 absolute error = 2.152775735453361e-10 relative error = 3.037858416992049e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.009999999999999343 y[1] (closed_form) = -7.072781645933373 y[1] (numeric) = -7.072781645714581 absolute error = 2.187912073736697e-10 relative error = 3.093425166030226e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.591949208711867e-16 y[1] (closed_form) = -7.059082159123578 y[1] (numeric) = -7.059082158901257 absolute error = 2.223217165919777e-10 relative error = 3.14944225864599e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.01000000000000066 y[1] (closed_form) = -7.045392878522046 y[1] (numeric) = -7.045392878296169 absolute error = 2.258770948060373e-10 relative error = 3.206025536129093e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000067 y[1] (closed_form) = -7.031713806261049 y[1] (numeric) = -7.031713806031599 absolute error = 2.29450236588491e-10 relative error = 3.263077009536254e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03000000000000068 y[1] (closed_form) = -7.018044944484847 y[1] (numeric) = -7.018044944251804 absolute error = 2.33042918296178e-10 relative error = 3.320624477894167e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000069 y[1] (closed_form) = -7.004386295349711 y[1] (numeric) = -7.004386295113053 absolute error = 2.366578044643575e-10 relative error = 3.378708633209981e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.0500000000000007 y[1] (closed_form) = -6.990737861023923 y[1] (numeric) = -6.990737860783633 absolute error = 2.40290454200931e-10 relative error = 3.437268840255669e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000071 y[1] (closed_form) = -6.977099643687822 y[1] (numeric) = -6.977099643443879 absolute error = 2.439435320411576e-10 relative error = 3.496345824182878e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000071 y[1] (closed_form) = -6.96347164553381 y[1] (numeric) = -6.963471645286194 absolute error = 2.476161498066176e-10 relative error = 3.555929605392049e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000072 y[1] (closed_form) = -6.949853868766386 y[1] (numeric) = -6.949853868515076 absolute error = 2.513100838541504e-10 relative error = 3.616048460868696e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000073 y[1] (closed_form) = -6.936246315602156 y[1] (numeric) = -6.936246315347131 absolute error = 2.550244460053364e-10 relative error = 3.676692470273051e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000007 y[1] (closed_form) = -6.922648988269866 y[1] (numeric) = -6.922648988011106 absolute error = 2.587601244385951e-10 relative error = 3.737877290572627e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000007 y[1] (closed_form) = -6.909061889010415 y[1] (numeric) = -6.909061888747901 absolute error = 2.625135664402478e-10 relative error = 3.799554420807883e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000008 y[1] (closed_form) = -6.895485020076892 y[1] (numeric) = -6.895485019810602 absolute error = 2.662901010808127e-10 relative error = 3.861803778929003e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000008 y[1] (closed_form) = -6.88191838373458 y[1] (numeric) = -6.881918383464495 absolute error = 2.700843992897717e-10 relative error = 3.924551036933487e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000008 y[1] (closed_form) = -6.868361982260994 y[1] (numeric) = -6.868361981987094 absolute error = 2.738991256023837e-10 relative error = 3.987837657796524e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000008 y[1] (closed_form) = -6.854815817945896 y[1] (numeric) = -6.854815817668161 absolute error = 2.777351681970686e-10 relative error = 4.051679513692525e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000008 y[1] (closed_form) = -6.841279893091326 y[1] (numeric) = -6.841279892809735 absolute error = 2.815916388954065e-10 relative error = 4.116066632206821e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000008 y[1] (closed_form) = -6.827754210011618 y[1] (numeric) = -6.827754209726147 absolute error = 2.85470314054237e-10 relative error = 4.181027981875042e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000008 y[1] (closed_form) = -6.814238771033423 y[1] (numeric) = -6.814238770744055 absolute error = 2.893685291383008e-10 relative error = 4.24652758527298e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000008 y[1] (closed_form) = -6.800733578495738 y[1] (numeric) = -6.800733578202452 absolute error = 2.932853959691784e-10 relative error = 4.312555293984189e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000008 y[1] (closed_form) = -6.787238634749932 y[1] (numeric) = -6.787238634452707 absolute error = 2.972253554389681e-10 relative error = 4.379179389939323e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000008 y[1] (closed_form) = -6.773753942159763 y[1] (numeric) = -6.773753941858577 absolute error = 3.01185743012411e-10 relative error = 4.446363797448185e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000008 y[1] (closed_form) = -6.760279503101406 y[1] (numeric) = -6.760279502796237 absolute error = 3.051683350463463e-10 relative error = 4.514137838625527e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000008 y[1] (closed_form) = -6.74681531996347 y[1] (numeric) = -6.746815319654301 absolute error = 3.091686906486757e-10 relative error = 4.582438913569516e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000009 y[1] (closed_form) = -6.733361395147043 y[1] (numeric) = -6.733361394833852 absolute error = 3.131903625330779e-10 relative error = 4.651322632983944e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000008 y[1] (closed_form) = -6.71991773106569 y[1] (numeric) = -6.719917730748455 absolute error = 3.172351270563922e-10 relative error = 4.720818613445777e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000008 y[1] (closed_form) = -6.706484330145499 y[1] (numeric) = -6.7064843298242 absolute error = 3.2129943150494e-10 relative error = 4.790877241906108e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000009 y[1] (closed_form) = -6.693061194825092 y[1] (numeric) = -6.693061194499709 absolute error = 3.253832758787212e-10 relative error = 4.861501582120591e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000009 y[1] (closed_form) = -6.679648327555661 y[1] (numeric) = -6.679648327226172 absolute error = 3.294893247129949e-10 relative error = 4.932734607505417e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000009 y[1] (closed_form) = -6.666245730800988 y[1] (numeric) = -6.666245730467371 absolute error = 3.336166898293413e-10 relative error = 5.004566337659674e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000009 y[1] (closed_form) = -6.652853407037465 y[1] (numeric) = -6.6528534066997 absolute error = 3.377653712277606e-10 relative error = 5.077000056403896e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000009 y[1] (closed_form) = -6.639471358754133 y[1] (numeric) = -6.639471358412198 absolute error = 3.41934480729833e-10 relative error = 5.150025691111582e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000009 y[1] (closed_form) = -6.626099588452695 y[1] (numeric) = -6.626099588106571 absolute error = 3.461240183355585e-10 relative error = 5.223646486369582e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000009 y[1] (closed_form) = -6.612738098647552 y[1] (numeric) = -6.612738098297215 absolute error = 3.503366485801962e-10 relative error = 5.297906001325648e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000009 y[1] (closed_form) = -6.599386891865819 y[1] (numeric) = -6.599386891511251 absolute error = 3.545679305716476e-10 relative error = 5.372740473947299e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000009 y[1] (closed_form) = -6.586045970647364 y[1] (numeric) = -6.586045970288541 absolute error = 3.588231933804309e-10 relative error = 5.448233962830372e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000009 y[1] (closed_form) = -6.572715337544821 y[1] (numeric) = -6.572715337181723 absolute error = 3.630979961144476e-10 relative error = 5.524322558750576e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000009 y[1] (closed_form) = -6.559394995123624 y[1] (numeric) = -6.559394994756232 absolute error = 3.67391450595278e-10 relative error = 5.600995989239917e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000009 y[1] (closed_form) = -6.54608494596204 y[1] (numeric) = -6.546084945590329 absolute error = 3.717106622502797e-10 relative error = 5.678366005310852e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.390000000000001 y[1] (closed_form) = -6.532785192651178 y[1] (numeric) = -6.53278519227513 absolute error = 3.760485256520951e-10 relative error = 5.756327731013066e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.400000000000001 y[1] (closed_form) = -6.519495737795036 y[1] (numeric) = -6.519495737414626 absolute error = 3.804094816928227e-10 relative error = 5.83495253302338e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.410000000000001 y[1] (closed_form) = -6.506216584010515 y[1] (numeric) = -6.506216583625722 absolute error = 3.847926421940429e-10 relative error = 5.914230447533792e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.420000000000001 y[1] (closed_form) = -6.492947733927451 y[1] (numeric) = -6.492947733538254 absolute error = 3.891971189773358e-10 relative error = 5.994151422837935e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.430000000000001 y[1] (closed_form) = -6.479689190188645 y[1] (numeric) = -6.479689189795022 absolute error = 3.936229120427015e-10 relative error = 6.074719025701322e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.440000000000001 y[1] (closed_form) = -6.466440955449886 y[1] (numeric) = -6.466440955051816 absolute error = 3.9807002139014e-10 relative error = 6.155936845826273e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.450000000000001 y[1] (closed_form) = -6.453203032379985 y[1] (numeric) = -6.453203031977444 absolute error = 4.025411115549105e-10 relative error = 6.23784978614644e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.460000000000001 y[1] (closed_form) = -6.439975423660794 y[1] (numeric) = -6.439975423253761 absolute error = 4.07032629823334e-10 relative error = 6.320406570619441e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.470000000000001 y[1] (closed_form) = -6.426758131987246 y[1] (numeric) = -6.426758131575701 absolute error = 4.115445761954106e-10 relative error = 6.403610774568782e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.480000000000001 y[1] (closed_form) = -6.413551160067376 y[1] (numeric) = -6.413551159651296 absolute error = 4.160805033848192e-10 relative error = 6.487521390262802e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.490000000000001 y[1] (closed_form) = -6.40035451062235 y[1] (numeric) = -6.400354510201712 absolute error = 4.206377468563005e-10 relative error = 6.572100750953545e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.500000000000001 y[1] (closed_form) = -6.387168186386496 y[1] (numeric) = -6.38716818596128 absolute error = 4.252163066098547e-10 relative error = 6.657352588838252e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.510000000000001 y[1] (closed_form) = -6.373992190107333 y[1] (numeric) = -6.373992189677518 absolute error = 4.298152944670619e-10 relative error = 6.743266725901403e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.520000000000001 y[1] (closed_form) = -6.360826524545601 y[1] (numeric) = -6.360826524111164 absolute error = 4.344373749631814e-10 relative error = 6.829888746167564e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.530000000000001 y[1] (closed_form) = -6.347671192475289 y[1] (numeric) = -6.347671192036203 absolute error = 4.390861008118918e-10 relative error = 6.917278597108134e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.540000000000001 y[1] (closed_form) = -6.334526196683662 y[1] (numeric) = -6.334526196239906 absolute error = 4.437552547642554e-10 relative error = 7.005342483176977e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.550000000000001 y[1] (closed_form) = -6.321391539971295 y[1] (numeric) = -6.321391539522851 absolute error = 4.484439486418523e-10 relative error = 7.094070123741911e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000011 y[1] (closed_form) = -6.308267225152101 y[1] (numeric) = -6.308267224698948 absolute error = 4.531530706231024e-10 relative error = 7.183479305003225e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000011 y[1] (closed_form) = -6.29515325505337 y[1] (numeric) = -6.295153254595482 absolute error = 4.578870616001041e-10 relative error = 7.27364439034967e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000011 y[1] (closed_form) = -6.282049632515781 y[1] (numeric) = -6.282049632053135 absolute error = 4.626459215728573e-10 relative error = 7.364569664941996e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000011 y[1] (closed_form) = -6.268956360393442 y[1] (numeric) = -6.268956359926021 absolute error = 4.674216569355849e-10 relative error = 7.456131931124965e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000011 y[1] (closed_form) = -6.255873441553934 y[1] (numeric) = -6.255873441081713 absolute error = 4.722213731156444e-10 relative error = 7.548448310654227e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000011 y[1] (closed_form) = -6.242800878878322 y[1] (numeric) = -6.242800878401276 absolute error = 4.770459582914555e-10 relative error = 7.641537309086317e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000011 y[1] (closed_form) = -6.229738675261189 y[1] (numeric) = -6.229738674779298 absolute error = 4.818909715709196e-10 relative error = 7.735332037033092e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000011 y[1] (closed_form) = -6.216686833610681 y[1] (numeric) = -6.216686833123921 absolute error = 4.867599656677157e-10 relative error = 7.829893618511313e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000011 y[1] (closed_form) = -6.203645356848524 y[1] (numeric) = -6.203645356356873 absolute error = 4.916511642250043e-10 relative error = 7.925197782014493e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000011 y[1] (closed_form) = -6.190614247910064 y[1] (numeric) = -6.1906142474135 absolute error = 4.965636790643657e-10 relative error = 8.021234390949241e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000011 y[1] (closed_form) = -6.177593509744298 y[1] (numeric) = -6.177593509242795 absolute error = 5.015028392563181e-10 relative error = 8.118093857507244e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000012 y[1] (closed_form) = -6.1645831453139 y[1] (numeric) = -6.164583144807438 absolute error = 5.064624275519236e-10 relative error = 8.215680048648847e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000012 y[1] (closed_form) = -6.151583157595259 y[1] (numeric) = -6.151583157083814 absolute error = 5.114451084864413e-10 relative error = 8.314040392268264e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000012 y[1] (closed_form) = -6.138593549578514 y[1] (numeric) = -6.138593549062063 absolute error = 5.164508820598712e-10 relative error = 8.413179303837956e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000012 y[1] (closed_form) = -6.125614324267577 y[1] (numeric) = -6.125614323746099 absolute error = 5.214779719153739e-10 relative error = 8.513072229334739e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000012 y[1] (closed_form) = -6.112645484680179 y[1] (numeric) = -6.112645484153649 absolute error = 5.265299307666282e-10 relative error = 8.6137815792891e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000012 y[1] (closed_form) = -6.099687033847889 y[1] (numeric) = -6.099687033316284 absolute error = 5.316049822567948e-10 relative error = 8.71528292036715e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000012 y[1] (closed_form) = -6.086738974816161 y[1] (numeric) = -6.086738974279458 absolute error = 5.367031263858735e-10 relative error = 8.817580786796983e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000012 y[1] (closed_form) = -6.073801310644354 y[1] (numeric) = -6.073801310102528 absolute error = 5.418261395107038e-10 relative error = 8.920708989297228e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000012 y[1] (closed_form) = -6.060874044405777 y[1] (numeric) = -6.060874043858806 absolute error = 5.469704689176069e-10 relative error = 9.024613692846232e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000012 y[1] (closed_form) = -6.047957179187718 y[1] (numeric) = -6.047957178635579 absolute error = 5.52138779141842e-10 relative error = 9.129343392871012e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000012 y[1] (closed_form) = -6.035050718091478 y[1] (numeric) = -6.035050717534148 absolute error = 5.573301820049892e-10 relative error = 9.234888123379997e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000012 y[1] (closed_form) = -6.022154664232406 y[1] (numeric) = -6.02215466366986 absolute error = 5.625455656854683e-10 relative error = 9.341267321256542e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000013 y[1] (closed_form) = -6.009269020739932 y[1] (numeric) = -6.009269020172147 absolute error = 5.677849301832794e-10 relative error = 9.448485801245872e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 Finished! diff ( y , x , 1 ) = arccos ( 0.1 * x + 0.2 ) ; Iterations = 1600 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %